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Answer:
(a) x = 260.52
(b) x = 249.24
(c) x = 265.22
(d) x = 297.65
Step-by-step explanation:
Here,
Mean = = 300
Standard deviation = = 47
(a) Using standard normal table,
P(Z > z) = 80%
1 - P(Z < z) = 0.8
P(Z < z) = 1 - 0.8
P(Z < -0.52) = 0.2
z = -0.84
Using z-score formula,
x = z × σ + μ
x = -0.84 × 47 + 300 = 260.52
(b) Using standard normal table,
P(Z < z) = 14%
P(Z < -1.08) = 0.1 4
z = -1.08
Using z-score formula,
x = z × σ + μ
x = -1.08 × 47 + 300 = 249.24
(c) Using standard normal table,
P(Z < z) = 23%
P(Z < -0.74) = 0.243
z = -0.714
Using z-score formula,
x = z × σ + μ
x = -0.74 × 47 + 300 = 265.22
(d) Using standard normal table,
P(Z > z) = 52%
1 - P(Z < z) = 0.52
P(Z < z) = 1 - 0.52
P(Z < -0.25) = 0.4 8
z = -0.05
Using z-score formula,
x = z × σ + μ
x = -0.05 × 47 + 300 = 297.65